问题 单项选择题

A是四阶矩阵,r(A)=3,又α1=(1,2,1,3)T,α2=(1,1,-1,1)T,α3=(1,3,3,5)T,α4=(-3, -5,-1,-6)T均是齐次线性方程组A*x=0的解向量,则A*x=0的基础解系是( ).

A.α1

B.α12

C.α123

D.α124

答案

参考答案:D

解析:
因A是四阶矩阵且r(A)=3,故r(A*)=1,于是A*x=0的基础解系应包括n-r(A*)= 4-1=3个线性无关的解向量.已知α1234均为齐次线性方程组A*x=0的解向量,故我们考查其秩是否为3.若r(α1234)=3,则它的一个极大无关组必为一个基础解系.由


得r=3.主元所在列为1,2,4,故α124为一个极大线性无关组.因此应选D.

选择题
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Like any awards ceremony of its age, the Oscars, now in its 85th year, has been trying hard to change.

So how did that go this year? When host Seth MacFarlane noted in his opening speech that it was the first time the Academy Awards had a theme, I thought: “well, that’s a good start.”

But when he revealed that the theme was a tribute to(向…致敬) musicals, I was less sure. After all, it’s not the first time that musicals have featured at the Oscars.

In 2007, the cast of Dream-girls gave a special performance directed by movie director and musical veteran(经验丰富的老手) Bill Condon. Then there was the memorable 2009 show hosted by Hugh Jackman, who screams musicals. With Beyonce Knowles and Anne Hathaway, he performed several hit songs from move musical. And in 2010, how did Neil Patrick Harris introduce the hosts? By performing a musical number.

So I guess the Oscars could have done better this year. But I must admit, there were more music performances in the three-and-a –half-hour show than ever before. This suggests the Oscars has dropped some of its arrogance and wants to offer audiences more entertainment.

It’s a timely move as the Golden Globes, also known as the “big party,” has become a threat to the Oscars, stealing viewers and even its reputation. Just look at the Oscars’ winning list this year.

You can’t blame the academy for wanting to stick it to the Golden Globes. While they hired Tina Fey and Amy Poehler to host the show—certainly more audience-friendly than MacFarlane— and Bill Clinton was invited as a presenter, who did viewers get at the Oscars? The First Lady of the US, Michelle Obama.

Way to go, Oscar! We know you’re struggling to look fresh and young, but don’t lose the pride and dignity that made you one biggest honor in the movie industry. Don’t ever let that change.

小题1:Examples are given in Para.4 to show that__________.

A.the Oscars has been trying hard to change

B.the Oscars’ theme is a tribute to musicals

C.it is not the first time that the Oscars has had a theme

D.musicals are not a new feature this year小题2:What disappoints the writer is that__________.

A.the Oscars didn’t invite Bill Clinton as a presenter

B.the show took as long as three and a half hours

C.the Oscars has lost some pride and dignity to cater to the audiences

D.the Oscars is no longer fresh and young小题3: Which of the following is true of the Golden Globes?

A.It gave an award to the First Lady of the US, Michelle Obama.

B.Its host and hostess had better reputation.

C.It has become highly competitive with the Academy Awards.

D.It is more friendly to the audience.小题4:Which of the following could be the best title for the passage?

A.Nothing new, but well done

B.So old, still young

C.New start, good change

D.Too old to change